Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes. Drain and mash.
Mix in butter and 1/4 cup shredded cheese. Season with salt and pepper to taste; set aside.
Bring a large pot of salted water to a boil. Add carrots and cook until almost tender but still firm, about 15 minutes. Drain, and set aside.
Preheat oven to 375 degrees F (190 degrees C.)
Heat oil in a large frying pan. Add onion, pepper, and ground beef and cook until well browned. Pour off excess fat, then stir in carrots,peas, and corn.
Stir in flour and cook 1 minute. Add ketchup and beef broth. Bring to a boil, reduce heat and simmer for 5 minutes.
Spread the ground beef mixture in an even layer on the bottom of a 12 inch cast iron skillet. Top with the mashed potato mixture and sprinkle with remaining shredded cheese.
Bake in the preheated oven for 20 minutes, or until golden brown.